Lattice-valued modal propositional logic and its completeness
- 54 Downloads
Based on the concept of the complete lattice satisfying the first and second infinite distributive laws, the present paper introduces the semantics of the lattice-valued modal propositional logic. It is pointed out that this semantics generalizes the semantics of both classical modal propositional logic and [0, 1]-valued modal propositional logic. The definition of the QMR 0-algebra is proposed, and both the Boole-typed latticevalued modal propositional logic system B and the QMR 0-typed lattice-valued modal propositional logic system QML* are constructed by use of Boole-algebras and QMR 0-algebras, respectively. The main results of the paper are the completeness theorems of both the system B and QML*.
Keywordslatticed-valued modal propositional logic modal model QMR0-algebra validity completeness
Unable to display preview. Download preview PDF.
- 3.Wang G J. Non-classical Mathematical Logic and Approximate Reasoning (in Chinese). 2nd ed. Beijing: Science Press, 2008. 224–251Google Scholar
- 4.Hájek P. On fuzzy modal logics S5(C). Fuzzy Sets Syst, 2009, doi: 10.1016/j.fss.2009.11.011Google Scholar
- 9.Wang G J, Zhou H J. Introduction to Mathematical Logic and Resolution Principle. Beijing: Science Press, Oxford, U.K. Alpha Science International Limited, 2009. 257–323Google Scholar
- 14.Wang D G, Gu Y D, Li H X. Generalized tautology in fuzzy modal propositional logic (in Chinese). Acta Electr Sin, 2003, 35: 261–264Google Scholar
- 15.Hu M D, Wang G J. Tautologies and quasi-tautologies in fuzzy modal logic (in Chinese). Acta Electr Sin, 2009, 37: 2484–2488Google Scholar
- 16.Wang G J. The Theory of Topological Molecular Lattices (in Chinese). Xi’an: Shaanxi Normal University Press, 1990. 5–7Google Scholar